2003 Spring Visit of CRSC to University of Paris VI

Once again a group of graduate students and post-docs from the CRSC
traveled to Paris for a research and cultural exchange. In April, 2003,
Dr. H. T. Banks and five of his advisees visited Universite de Paris VI.
The group was warmly welcomed by Alain Damlamian, Doina Cioranescu, and
many other faculty and students at Paris VI.

In addition to the traditional sight-seeing, taste-testing, and relaxing
outside of sidewalk cafes, the students participated in several
intellectual discussions with their Parisian counterparts. The
conversations were mostly research-oriented and scientific in nature, but
occassionally drifted toward politics (considering the strained relations between
the respective governments at the time). In exchange for a detailed and
exhaustive summary of current student research at Paris VI, the CRSC
representatives offered the following presentations (click to see the
abstracts):

Ecologists studying insect pest control are interested in the potentially
combined effects of pesticide application and environmental factors
including the presence of surrounding vegetation and natural predators. We
consider several population dynamics models in investigating data from
controlled experiments with aphids in broccoli patches surrounded by
different margin types (bare ground or weedy) and three levels of
insecticide spray (no, light, or heavy spray). We carry out parameter
estimation computations along with statistical analysis to compare
autonomous versus nonautonomous model dynamics. We offer a positive
example of how one might combine a priori biological hypothesis and
intuition with rather sophisticated (from a field biology viewpoint)
mathematical methodologies to investigate pesticide-environment synergisms.
This work involves collaborations with field zoologists
J.E.Banks(University of Washington -- Tacoma) and J. D. Stark (Washington
State University).

Brandy Benedict --
Inverse Problems in Electromagnetic Interrogation

ABSTRACT

Electromagnetic interrogation is a technique in which reflected
electromagnetic waves incident upon a dielectric medium are observed
and evaluated to determine material properties of the dielectric. We
describe the general inverse problem and briefly present previous
theoretical results. Various input waves (i.e., truncated sine,
truncated square waves) are compared in one-dimensional forward
computational simulations. An apparatus for experimental testing and
verification of the previously developed theory is discussed in detail.

We consider the problem of detecting a crack inside of a dielectric
material using electromagnetic interrogation. The technique is to measure
the reflected and/or transmitted signals, and solve a parameter identification
problem to determine the dimensions of any gaps. Details of the problem
formulation, discussion of numerical methods, and computational results
will be presented.

Our goal is the solution of certain inverse scattering problems for
dispersive dielectrics in the time domain and in two spatial
dimensions. Achieving this goal requires the ability to obtain fast and
accurate solutions of Maxwell's equations. To this end, the
finite-difference time-domain (FDTD) method is used. As opposed to other
approaches, the solution of a linear system is not required at each time
step. A dramatic increase in speed for a forward calculation is therefore
obtained. In addition, implementation of the Perfectly Matched Layer (PML)
absorbing boundary condition is straightforward, and is highly effective in
reducing reflections off of the computationally induced boundaries. We will
discuss some important implementation details of this approach. Our goal
of solving certain inverse scattering problems for dispersive dielectrics
motivates us to seek solutions of Maxwell's equations that are not only
accurate, but are fast.

Nicholas Luke --
Active Sound Field Attenuation via Acoustic Arrays

ABSTRACT

We formulate a model for suppression of a diffusive random acoustic field
using arrays of micro-acoustic actuators as an active control surface.
Boundary dissipation is effected by a proportional feedback gain described
by a distributed shape function. A computational method based on Fourier
transforms is developed and analyzed as to its effectiveness in providing
decay rates for various gains. Several geometries are discussed.